On Topological Classification of Non-Archimedean Fréchet Spaces

Author： Śliwa Wiesław  

Publisher： Springer Publishing Company

ISSN： 0011-4642

Source： Czechoslovak Mathematical Journal, Vol.54, Iss.2, 2004-06, pp. : 457-463

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Abstract

We prove that any infinite-dimensional non-archimedean Fréchet space E is homeomorphic to d^{\bbb n} where D is a discrete space with card(D) = dens(E). It follows that infinite-dimensional non-archimedean Fréchet spaces E and F are homeomorphic if and only if dens(E) = dens(F). In particular, any infinite-dimensional non-archimedean Fréchet space of countable type over a field {\bbb k} is homeomorphic to the non-archimedean Fréchet space {\bbb k}^{\bbb n}.

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